diff --git a/python/ql/src/Classes/IncompleteOrdering.ql b/python/ql/src/Classes/IncompleteOrdering.ql
index d6cd1230ece..bbb6ca5cf6d 100644
--- a/python/ql/src/Classes/IncompleteOrdering.ql
+++ b/python/ql/src/Classes/IncompleteOrdering.ql
@@ -2,7 +2,8 @@
  * @name Incomplete ordering
  * @description Class defines one or more ordering method but does not define all 4 ordering comparison methods
  * @kind problem
- * @tags reliability
+ * @tags quality
+ *       reliability
  *       correctness
  * @problem.severity warning
  * @sub-severity low
@@ -11,63 +12,46 @@
  */
 
 import python
+import semmle.python.dataflow.new.internal.DataFlowDispatch
+import semmle.python.ApiGraphs
 
-predicate total_ordering(Class cls) {
-  exists(Attribute a | a = cls.getADecorator() | a.getName() = "total_ordering")
+predicate totalOrdering(Class cls) {
+  cls.getADecorator() =
+    API::moduleImport("functools").getMember("total_ordering").asSource().asExpr()
+}
+
+Function getMethod(Class cls, string name) {
+  result = cls.getAMethod() and
+  result.getName() = name
+}
+
+predicate definesStrictOrdering(Class cls, Function meth) {
+  meth = getMethod(cls, "__lt__")
   or
-  exists(Name n | n = cls.getADecorator() | n.getId() = "total_ordering")
+  not exists(getMethod(cls, "__lt__")) and
+  meth = getMethod(cls, "__gt__")
 }
 
-string ordering_name(int n) {
-  result = "__lt__" and n = 1
+predicate definesNonStrictOrdering(Class cls, Function meth) {
+  meth = getMethod(cls, "__le__")
   or
-  result = "__le__" and n = 2
+  not exists(getMethod(cls, "__le__")) and
+  meth = getMethod(cls, "__ge__")
+}
+
+predicate missingComparison(Class cls, Function defined, string missing) {
+  definesStrictOrdering(cls, defined) and
+  not definesNonStrictOrdering(getADirectSuperclass*(cls), _) and
+  missing = "__le__ or __ge__"
   or
-  result = "__gt__" and n = 3
-  or
-  result = "__ge__" and n = 4
+  definesNonStrictOrdering(cls, defined) and
+  not definesStrictOrdering(getADirectSuperclass*(cls), _) and
+  missing = "__lt__ or __gt__"
 }
 
-predicate overrides_ordering_method(ClassValue c, string name) {
-  name = ordering_name(_) and
-  (
-    c.declaresAttribute(name)
-    or
-    exists(ClassValue sup | sup = c.getASuperType() and not sup = Value::named("object") |
-      sup.declaresAttribute(name)
-    )
-  )
-}
-
-string unimplemented_ordering(ClassValue c, int n) {
-  not c = Value::named("object") and
-  not overrides_ordering_method(c, result) and
-  result = ordering_name(n)
-}
-
-string unimplemented_ordering_methods(ClassValue c, int n) {
-  n = 0 and result = "" and exists(unimplemented_ordering(c, _))
-  or
-  exists(string prefix, int nm1 | n = nm1 + 1 and prefix = unimplemented_ordering_methods(c, nm1) |
-    prefix = "" and result = unimplemented_ordering(c, n)
-    or
-    result = prefix and not exists(unimplemented_ordering(c, n)) and n < 5
-    or
-    prefix != "" and result = prefix + " or " + unimplemented_ordering(c, n)
-  )
-}
-
-Value ordering_method(ClassValue c, string name) {
-  /* If class doesn't declare a method then don't blame this class (the superclass will be blamed). */
-  name = ordering_name(_) and result = c.declaredAttribute(name)
-}
-
-from ClassValue c, Value ordering, string name
+from Class cls, Function defined, string missing
 where
-  not c.failedInference(_) and
-  not total_ordering(c.getScope()) and
-  ordering = ordering_method(c, name) and
-  exists(unimplemented_ordering(c, _))
-select c,
-  "Class " + c.getName() + " implements $@, but does not implement " +
-    unimplemented_ordering_methods(c, 4) + ".", ordering, name
+  not totalOrdering(cls) and
+  missingComparison(cls, defined, missing)
+select cls, "This class implements $@, but does not implement an " + missing + " method.", defined,
+  defined.getName()